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Display information for equation id:math.1604.29 on revision:1604

* Page found: Allgemeine Eigenschaften der stationären Zustände (eq math.1604.29)

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Allgemeine Eigenschaften der stationären Zustände Eq: math.1604.29

Hash: 9b78d0deeada4be5fdd29fe21ca78063

TeX (original user input):

\begin{align}
& \sum\limits_{i=1}^{3}{{}}\left[ -\frac{{{\hbar }^{2}}}{2m}\frac{{{\partial }^{2}}}{\partial {{x}_{i}}^{2}}+{{V}_{i}}({{x}_{i}}) \right]{{\phi }_{1}}({{x}_{1}}){{\phi }_{2}}({{x}_{2}}){{\phi }_{3}}({{x}_{3}})=E{{\phi }_{1}}({{x}_{1}}){{\phi }_{2}}({{x}_{2}}){{\phi }_{3}}({{x}_{3}}) \\
& \Rightarrow \frac{\frac{{{\hbar }^{2}}}{2m}{{\phi }_{i}}\acute{\ }\acute{\ }({{x}_{i}})+{{V}_{i}}({{x}_{i}}){{\phi }_{i}}({{x}_{i}})}{{{\phi }_{i}}({{x}_{i}})}={{E}^{(i)}} \\
\end{align}

TeX (checked):

{\begin{aligned}&\sum \limits _{i=1}^{3}{}\left[-{\frac {{\hbar }^{2}}{2m}}{\frac {{\partial }^{2}}{\partial {{x}_{i}}^{2}}}+{{V}_{i}}({{x}_{i}})\right]{{\phi }_{1}}({{x}_{1}}){{\phi }_{2}}({{x}_{2}}){{\phi }_{3}}({{x}_{3}})=E{{\phi }_{1}}({{x}_{1}}){{\phi }_{2}}({{x}_{2}}){{\phi }_{3}}({{x}_{3}})\\&\Rightarrow {\frac {{\frac {{\hbar }^{2}}{2m}}{{\phi }_{i}}{\acute {\ }}{\acute {\ }}({{x}_{i}})+{{V}_{i}}({{x}_{i}}){{\phi }_{i}}({{x}_{i}})}{{{\phi }_{i}}({{x}_{i}})}}={{E}^{(i)}}\\\end{aligned}}

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MathML (4.609 KB / 627 B) :

\begin{aligned} \sum_{i = 1}^{3} [- \frac{ℏ^{2}}{2 m} \frac{\partial^{2}}{\partial {x_{i}}^{2}} + V_{i} (x_{i})] ϕ_{1} (x_{1}) ϕ_{2} (x_{2}) ϕ_{3} (x_{3}) = E ϕ_{1} (x_{1}) ϕ_{2} (x_{2}) ϕ_{3} (x_{3}) \\ \Rightarrow \frac{\frac{ℏ^{2}}{2 m} ϕ_{i} \overset{´}{} \overset{´}{} (x_{i}) + V_{i} (x_{i}) ϕ_{i} (x_{i})}{ϕ_{i} (x_{i})} = E^{(i)} \end{aligned}

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Identifiers

$i$

$m$

$x_{i}$

$V_{i}$

$x_{i}$

$ϕ_{1}$

$x_{1}$

$ϕ_{2}$

$x_{2}$

$ϕ_{3}$

$x_{3}$

$E$

$ϕ_{1}$

$x_{1}$

$ϕ_{2}$

$x_{2}$

$ϕ_{3}$

$x_{3}$

$m$

$ϕ_{i}$

$\overset{´}{}$

$\overset{´}{}$

$x_{i}$

$V_{i}$

$x_{i}$

$ϕ_{i}$

$x_{i}$

$ϕ_{i}$

$x_{i}$

$E$

$i$

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